Lesson 5
More Dilations
Problem 1
Quadrilateral \(ABCD\) is dilated with center \((0,0)\), taking \(B\) to \(B'\). Draw \(A'B'C'D'\).
![A quadrilateral, A, negative 2 comma 3, B, 3 comma 1, C, 1 comma negative 1, D, negative 3 comma negative 2. Another point, B prime, 6 comma 2.](https://cms-im.s3.amazonaws.com/kMSntvCPDjZzU1hHntfmoCC5?response-content-disposition=inline%3B%20filename%3D%228-8.2.A.PP.Image.10.3.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.A.PP.Image.10.3.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T233904Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=a65e10ca5c247ac82f9e2ef2b736a7dbbf0ba0d026e6fdc23a759f90871cc8a2)
Solution
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Problem 2
Triangles \(B\) and \(C\) have been built by dilating Triangle \(A\).
![Three triangles, 2 of which are dilations of the first. Please ask for further assistance.](https://cms-im.s3.amazonaws.com/QhQZu4dyyfAhnaAfJWh41pHH?response-content-disposition=inline%3B%20filename%3D%228.2.A5.newPP.Image.01%20%25281%2529.png%22%3B%20filename%2A%3DUTF-8%27%278.2.A5.newPP.Image.01%2520%25281%2529.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T233904Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=f730dc20fe2eff8ed54c14a2061e4908d926134702d23d72cdc5de42ed225475)
- Find the center of dilation.
- Triangle \(B\) is a dilation of \(A\) with approximately what scale factor?
- Triangle \(A\) is a dilation of \(B\) with approximately what scale factor?
- Triangle \(B\) is a dilation of \(C\) with approximately what scale factor?
Solution
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Problem 3
Here is a triangle.
- Draw the dilation of triangle \(ABC\), with center \((0,0)\), and scale factor 2. Label this triangle \(A’B’C’\).
- Draw the dilation of triangle \(ABC\), with center \((0,0)\), and scale factor \(\frac{1}{2}\). Label this triangle \(A’’B’’C’’\).
- Is \(A’’B’’C’’\) a dilation of triangle \(A’B’C’\)? If yes, what are the center of dilation and the scale factor?
![Coordinate plane, x, negative 7 to 8, y, negative 6 to 6. A triangle, A, 4 comma negative 2, B, negative 2 comma negative 2, C, negative 2 comma 2.](https://cms-im.s3.amazonaws.com/GxLShQ5qMCVtpj9oTygKTaRj?response-content-disposition=inline%3B%20filename%3D%228-8.2.A.PP.Image.22.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.A.PP.Image.22.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T233904Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=a08d437507caed4208731b4f540ef073fa22e17fd519d97947770a0e7bd6a28a)
Solution
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Problem 4
Triangle \(DEF\) is a right triangle, and the measure of angle \(D\) is \(28^\circ\). What are the measures of the other two angles?
Solution
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(From Unit 1, Lesson 15.)